In order to be able to act on a target object, it is necessary to be able to precisely capture and track the target object. Optical target acquisition systems, for example, are known from the prior art for this purpose, which are aimed at the target and held thereon by means of high-precision mechatronic positioning systems. Only then can the target be acted on. If the point of accuracy which must be achieved in order to engage the target is a few microrad, for example when aiming a laser beam at the target, the problem often occurs, especially in the case of quickly moving objects or objects which are highly agile and can change their trajectory, that the necessary precision cannot be achieved with a single positioning system or can only be realized with considerable effort. This is especially true if, in addition, the largest possible range of angles is to be covered by the positioning system. Various examples are known from the literature in which the precision to be achieved from the total system is attained by means of cascading positioning system levels with increasing precision (DE 4122623 A1, U.S. Pat. No. 7,171,126 B2). The challenge in operating these cascading total systems is in combining the sensor information present in the system such that the target can always be tracked with the highest precision.